Long divsion (synthetic style) help?? BLAH...I cant figure it out?

Question

well, here it is. Beem trying for 1 hour to try and get an answer, but the computer keeps marking me wrong. Gosh.

Help?

http://online.math.uh.edu/webct/spring06/1310/q9/images/q9_problem19__25.gif

there it is.

Answer 1

EDITED 11/6 PLEASE NOTE: There was a sign error in the initial answer that has been corrected.

Write it out as a long division problem:
..............______________
x^3-x+8 | x^4+3x^2+9x+6

Start by dividing the x^3 into the x^4 to get x, so the first term of the quotient is x. Put it on top like you do in regular long division:

................x
..............______________
x^3-x+8 | x^4+3x^2+9x+6

Now multiply the divisor by the x term to get x^4-x^2+8x, put that under the dividend, aligning terms of like power:


................x
..............______________
x^3-x+8 | x^4+3x^2+9x+6
................x^4-x^2..+8x

Now, just as in ordinary divistion, subract the underneath term from the dividend. The x^4 terms will subtract out. leaving the other difference terms:

...............x
..............______________
x^3-x+8 | 4x^2+x+6


Now repeat the process, dividing x^3 into 4x^2 to get 4x^-1 as the next term ot the quotient. The quotient now is x+4x^-1. When you multiply and subtract again, the 4x^2 term subtracts out. Continue this until you reach the last term of the dividend, and whatever is left from the last subtraction is your remainder.